Improvement of Incomplete Multiview Clustering by the Tensor Reconstruction of the Connectivity Graph

H. Zhang; Жанг Х.; X. Chen; Чен С.; Yu. Zhu; Жу Ю.; I. A. Matveev; Матвеев И. А.

doi:10.31857/S0002338823030137

Improvement of Incomplete Multiview Clustering by the Tensor Reconstruction of the Connectivity Graph

Authors: Zhang H.¹, Chen X.¹, Zhu Y.², Matveev I.A.³
Affiliations:
1. College of Mathematics, Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, China
2. Fundamental Experimental Teaching Department, Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, China
3. Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 119333, Moscow, Russia
Issue: No 3 (2023)
Pages: 14-37
Section: КОМПЬЮТЕРНЫЕ МЕТОДЫ
URL: https://journals.rcsi.science/0002-3388/article/view/136862
DOI: https://doi.org/10.31857/S0002338823030137
EDN: https://elibrary.ru/EVCFML
ID: 136862

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Abstract
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Abstract

With the development of data collection technologies, a significant volume of multiview data has appeared, and their clustering has become topical. Most methods of multiview clustering assume that all views are fully observable. However, in many cases this is not the case. Several tensor methods have been proposed to deal with incomplete multiview data. However, the traditional tensor norm is computationally expensive, and such methods generally cannot handle undersampling and imbalances of various views. A new method for clustering incomplete multiview data is proposed. A new tensor norm is defined to reconstruct the connectivity graph, and the graphs are regularized to a consistent low-dimensional representation of patterns. The weights are then iteratively updated for each view. Compared to the existing ones, the proposed method not only determines the consistency between views but also obtains a low-dimensional representation of the samples using the resulting projection matrix. An efficient optimization algorithm based on the method of indefinite Lagrange multipliers is developed for the solution. The experimental results on four data sets demonstrate the effectiveness of the method.

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